A new locking-free shear deformable finite element based on absolute nodal coordinates

García-Vallejo, Daniel; Mikkola, Aki; Escalona, José L.

doi:10.1007/s11071-006-9155-4

Cited by 89 publications

(31 citation statements)

References 27 publications

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“…Dufva and Shabana [7] eliminated secondorder slope vectors leading to a more efficient reducedorder element for thin plate element. ANCF elements considering transverse shear deformation and related shear locking problem have been studied by Omar and Shabana [8], Sopanen and Mikkola [9], Dufva, Sopanen, and Mikkola [10], Garcia-Vallejo, Mikkola and Escalona [11]. Shear locking can also present in solid elements when applied to thin-walled structures [12], and the reduced integration or higher order elements should be employed for such application.…”

Section: Introductionmentioning

confidence: 99%

Integration of absolute nodal elements into multibody system

et al. 2010

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In this paper, a short summary of the formulation of absolute nodal coordinates elements, including beam, plate, and large deformation solid elements, is given and two aspects of the integration of the elements into a general-purpose flexible multibody system, i.e., constraints and contacts, are studied. As an alternative to the constraint method for coupling flexible and rigid bodies, the direct assembling of nodal absolute coordinates into those of rigid body's is proposed to simultaneously reduce the number of system generalized coordinates and constraint equations. To enable the contacts between flexible and rigid bodies, the shape of contacting bodies are represented with basic geometries including sphere, brick, cylinder, and triangular patches, and the collision detections between bodies are converted into those of basic geometries or tessellated triangular meshes of the outer surface. Several numerical examples are carried out to demonstrate the effectiveness of presented methods.

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Section: Introductionmentioning

confidence: 99%

Integration of absolute nodal elements into multibody system

et al. 2010

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“…The presence of curvature locking in shear deformable ANCF elements has previously been discussed in the context of beam elements [26]. Here it was concluded that two noded shear deformable ANCF beam elements will suffer from curvature locking when they have non-parallel transverse slope vectors, as shown in Fig.…”

Section: Assessment Of Curvature Thickness Lockingmentioning

confidence: 73%

“…Here several different combinations of generalized coordinates and stiffness descriptions have been investigated. These extensive studies have led to reports and treatment of severe problems with different locking mechanisms [26]. Because of the intensive work of enhancing the ANCF beam el-3.…”

Section: Absolute Nodal Coordinate Formulationmentioning

confidence: 99%

“…Here, the inplane slope vectors are omitted from the generalized coordinates, leading to a kinematic description based on the nodal positions and transverse slope vectors. This choice of parameterization has also been used for modeling of shear deformable beam elements with success [26]. Using this, the element is still capable of describing transverse shear and thickness deformation, but the total number of element d.o.f.…”

Section: Shear and Thickness Deformable Ancf Shell Elementsmentioning

confidence: 99%

“…Using this, the element is capable of describing curvature correctly and an significant improvement in accuracy was demonstrated [26].…”

Section: Assessment Of Curvature Thickness Lockingmentioning

confidence: 99%

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Rectangular shell elements based on the absolute nodal coordinate formulation

Hyldahl¹

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This thesis concerns the development of tools that are useful for designing machine systems and components in an virtual environment using flexible multibody dynamics. Initially, flexible multibody dynamics is briefly reviewed to explain available formalisms and possible applications of this method. Subsequently, attention is turned towards the analysis of structures that undergo large deformations and rotations using shell finite elements based on the absolute nodal coordinate formulation, ANCF. This topic is the focus for the remainder of the thesis.The thesis is divided into three main parts. The first part acts as a general introduction to ANCF based shell finite elements and sums up available elements found in the research literature. In the end, a new ANCF element developed during this PhD project is presented which gives enhanced modeling capabilities of problems including e.g. moving boundary conditions. The second part concerns the performance and behavior of a certain class of ANCF shell elements that are developed for analysis of thin shell structures. This includes discussions on differences concerning their kinematic descriptions and disclosure of certain issues regarding their performance. Those being sensitivity to irregular mesh, pour representation of curved structures and load dependent convergence when analyzing curved structures.The final part concerns the development of a new versatile ANCF shell element. This element is distinguished by being able to describe both thin and thick curved structures. This part contains a thorough derivation of its kinematics and stiffness description, as well as numerical examples to demonstrate its performance. However, this part of the study is not yet complete.Finally, the findings of this PhD project are summed up in a conclusion and possibilities for further studies and perspectives are outlined.v ResuméDenne afhandling omhandler udviklingen af vaerktøjer, som er nyttige til at designe maskiner og maskindele i et virtuelt miljø vha. fleksibel flerlegemedynamik. Indledningsvist gives der en kort gennemgang af den fleksible flerlegeme-dynamik, for at give et overblik over metoden og dens mulige anvendelser. Dernaest flyttes opmaerksomheden over på analyse af strukturer som udsaettes for store deformationer og rotationer vha. endelige skalelementer (eng: shell finite elements) baseret på absolutte knude koordinater (eng: absolute nodal coordinate formulation, ANCF). Dette emne vil vaere fokus i resten af afhandlingen.Afhandlingen er inddelt i 3 dele. Den første del giver en general introduktion til ANCF skal-elementer, og opsummerer de forskellige elementklasser som kan findes i litteraturen. Mod slutningen introduceres der et nyt ANCF skal-element, som er udviklet under dette ph.d.-projekt. Dette element muliggør forbedret modellering af problemer med mobile randbetingelser.Anden del omhandler effektiviteten og egenskaberne hos en saerlig klasse af ANCF skal-elementer, som er udviklet specielt til analyse af tynde skalstrukturer. Heri diskuteres der...

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The Absolute Nodal Coordinate Formulation

Gerstmayr

Humer

Gruber

et al. 2016

Structure-Preserving Integrators in Nonlinear Structural Dynamics and Flexible Multibody Dynamics

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The key idea of the absolute nodal coordinate formulation (ANCF) is to use slope vectors in order to describe the orientation of the cross-section of structural mechanics components, such as beams, plates or shells. This formulation relaxes the kinematical assumptions of Bernoulli-Euler and Timoshenko beam theories and enables a deformation of the cross-sections. The present contribution shows how to create 2D and 3D structural finite elements based on the ANCF by employing different sets of slope vectors for approximating the cross-sections' orientation. A specific aim of this chapter is to present a unified notation for structural mechanics and continuum mechanics ANC formulations. Particular focus is laid on enhanced formulations for such finite elements that circumvent severe issues like Poisson or shear locking. The performance of these elements is evaluated and a detailed assessment comprising the convergence order, the number of iterations, and Jacobian updates for large deformation benchmark problems is provided.

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A new locking-free shear deformable finite element based on absolute nodal coordinates

Cited by 89 publications

References 27 publications

Integration of absolute nodal elements into multibody system

Integration of absolute nodal elements into multibody system

Rectangular shell elements based on the absolute nodal coordinate formulation

The Absolute Nodal Coordinate Formulation

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